(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a large plane wall of thickness L = 0.4m, thermal conductivity k = 1.8W/(m*K), and surface area A = 30m2. The left side of the wall is maintained at a constant temperature of T1 = 90 C while the right side looses heat by convection to the surrounding air at Ts = 25 C with a heat transfer coefficient of h = 24 W(m2*K). Assuming constant thermal conductivity and no heat generation in the wall evaluate the rate of heat transfer through the wall.

Answer: 7079 W

My answer doesn't match the book's answer.

2. Relevant equations

[tex]\dot{Q}_{wall} = -kA\frac{dT(0)}{dx}[/tex]

[tex]\frac{d^2T}{dx^2} = 0[/tex]

[tex]T(0) = 90[/tex]

[tex]-k\frac{dT(L)}{dx} = h[T(L) - Ts][/tex]

3. The attempt at a solution

Solving the differential equation and applying B.C.:

[tex]T(x) = xC_1 + C_2[/tex]

[tex]T(0) = C_2 = 90[/tex]

[tex]-kC_1 = hLC_1+hC_2-25h][/tex]

[tex]C_1 = -\frac{h(C_2-25)}{k+hL}[/tex]

Plugging numbers in:

[tex]C_2 = 90[/tex]

[tex]C_1 = -136.8[/tex]

[tex]T(x) = 90-136.8x[/tex]

[tex]\dot{Q}_{wall} = -1.8*30*(-136.8) = 7,387 W[/tex]

Did I make a mistake or is the book's answer wrong?

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# Heat Transfer Through a Plane Wall

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